Ryan Ellis bounced a puck past Price for the tying goal in the third, then Filip Forsberg scored a power-play goal at 1:54 of overtime as the Predators rallied to beat the Canadiens 3-2 Tuesday night in a game between two of the NHL's top teams.
"Tonight was just one of those nights we needed a bounce, and fortunately we got it," Ellis said. "I think we played good enough to win and get other goals, but their goalie is one of the best in the league and he played well, too."
Pekka Rinne made 27 saves for his 39th win. He pulled within a victory of Price in this showdown between the league's winningest goalies this season.
Mattias Ekholm also scored for the Predators, who stayed a point behind first-place St. Louis in the Central Division. Mike Ribeiro had two assists.
Nashville won consecutive games for the first time since Feb. 22 and Feb. 24, after going 3-6-1 over the previous 10.
"Everyone is fighting for home ice right now, fighting to make the playoffs. Everyone is fighting for something," coach Peter Laviolette said. "We knew it was going to be a tough game. They have had an excellent year and played well tonight. Our guys are confident we can be successful even when we are down one in the third."
Brendan Gallagher and David Desharnais scored in the second period for Montreal, which had won three in a row. With the point, the Canadiens became the first NHL team to reach 100 this season as they try to hold off second-place Tampa Bay in the Atlantic Division.
P.K. Subban tripped Forsberg after the Predators forward forced a turnover, drawing a penalty 1:09 into overtime. Nashville capitalized quickly with Forsberg's wrister for his 22nd goal this season.
"To win a hockey game, you need some breaks, and that's a fact," Montreal coach Michel Therrien said. "They had a good break in the third period with their second goal, and even in overtime with P.K.'s penalty."
This was the first of four games in six days for the Predators, who set a franchise record with their 26th sellout of the season.
Nashville took a 1-0 lead when Ekholm got the puck and skated up the slot only to be tripped. He stayed with the puck and scored, shooting from his knees from in front of Price at 9:10 of the first.
The Canadiens took the lead by scoring twice in the second period.
Gallagher scored on a wrister from in front of Rinne at 2:28. Nashville captain Shea Weber was trying to clear the puck out of the corner when Pierre-Alexandre Parenteau slid the puck cross-ice to Desharnais, who beat Rinne with a snap shot at 12:42 for his 13th this season.
In the third, the Predators got a lucky bounce. Ribeiro sent the puck around the boards, and Ellis' wrister from the blue line bounced off the ice and past Price, tying it 2-all at 7:56.
It was Ellis' career-best seventh goal this season.
Price and Rinne both made some strong saves to force the game to overtime, including Price on a snap shot from Predators forward Mike Santorelli with less than four minutes left in regulation.
But the Predators got their fourth man advantage in overtime, and that was all they needed.
"It was a really fun hockey game to play in," Price said. "Obviously, we don't like the outcome, but you aren't going to win them all. You have to tip your hat to the Preds. They played a very good game tonight."
NOTES: The Canadiens reached 100 points for the 18th time and in consecutive seasons for the first time since 1987-88 and 1988-89. ... Predators forward Colin Wilson got the 100th assist of his career on Ellis' goal. ... Nashville called up Kevin Fiala, the 11th pick in the 2014 draft, from Milwaukee of the AHL under emergency conditions. He became the fourth 18-year-old to play for the Predators, who needed him because they scratched six players.